1. Field of the Invention
The present invention generally relates to an optical scanning lens, an optical scanning device and an image forming apparatus.
2. Description of the Related Art
An optical scanning device, which deflects a light flux from a light source at a uniform angular velocity by a light deflector having a deflection reflecting surface, converges the deflected light flux on a surface to be scanned as a beam spot by a scanning and image forming optical system, and, thus, scans the surface to be scanned at a uniform velocity with the beam spot, is well-known in relation to xe2x80x98image forming apparatusxe2x80x99 such as a digital copier, an optical printer, a laser plotter, a digital plate maker and so forth.
FIG. 1 illustrates one example of an optical scanning device.
A divergent light flux emitted by a semiconductor laser 10 is transformed into a light flux form (such as a parallel light flux or the like) suitable for subsequent optical systems by a coupling lens 12, passes through an opening of an aperture 14 so as to undergo xe2x80x98beam formationxe2x80x99, and is reflected by a mirror 18, while being converged in sub-scanning directions by a cylinder lens 16, and an approximately line-like image long in main-scanning directions is formed in the vicinity of a deflection reflecting surface of a rotational polygonal mirror 20. The light flux reflected by the deflection reflecting surface is incident on a scanning and image forming optical system 30 while being deflected at a uniform angular velocity as the rotational polygonal mirror 20 rotates at a uniform velocity, and is gathered in the vicinity of a surface to be scanned (actually, a photosensitive surface of a photoconductive photosensitive body or the like) 40 by a function of the optical system 30, and, thereby, a beam spot is formed on the surface to be scanned 40. By the beam spot, the surface to be scanned 40 is scanned in main scanning directions. The photosensitive surface which embodies the surface to be scanned 40 is moved in a sub-scanning direction (direction perpendicular to the plane of FIG. 1), and, the above-mentioned optical scanning is repeated. Thereby, a latent image is written on the photosensitive surface. A velocity of the above-mentioned optical scanning by a beam spot is made uniform by a function of a velocity uniformizing character of the scanning and image forming optical system 30.
Throughout the specification and claims, xe2x80x98an optical scanning lensxe2x80x99 is used in the above-described scanning and image forming optical system. In the example FIG. 1, the scanning and image forming optical system 30 consists of a single lens. In this case, the scanning and image forming optical system 30 itself is an optical scanning lens. When a scanning and image forming optical system consists of a plurality of optical elements (a plurality of single lenses, a lens and a concave mirror or the like), one or a plurality of single lenses used therein is an optical scanning lens.
As an optical scanning lens used in a scanning and image forming optical system, a lens obtained as a result of molding of plastic material has been used.
One problem occurring when an optical scanning lens is formed by molding plastic material is that a refractive-index distribution develops inside the thus-formed optical scanning lens.
In plastic molding, a plastic material, melted by heat, is molded by a metal die, and is cooled in the metal die. In this process, cooling of the material is fast in the periphery in comparison to the middle of the metal die. Thereby, a non-uniform distribution (the density of a fast-cooled portion is higher than the density of a slowly-cooled portion) in density and/or modification develops in the plastic. Thereby, the refractive index of the thus-formed lens is not uniform, and, thus, a refractive-index distribution develops therein.
FIGS. 2A through 2E illustrate such a refractive-index distribution. FIG. 2A shows a refractive-index distribution of an optical scanning lens 30 as a scanning and image forming optical system shown in FIG. 1 by contour lines in a section taken along a plane including the optical axis thereof and parallel to main scanning directions, and FIG. 2B shows a refractive-index distribution of that shown in FIG. 2A in directions perpendicular to the optical axis and parallel to the main scanning directions. FIG. 2C shows a refractive-index distribution of the optical scanning lens 30 by contour lines in a section taken along a plane including the optical axis thereof and parallel to sub-scanning directions, FIG. 2D shows a refractive-index distribution of that shown in FIG. 2C in directions parallel to the optical axis (axial directions), and FIG. 2E shows a refractive-index distribution of that shown in FIG. 2C in directions perpendicular to the optical axis and parallel to the sub-scanning directions.
As shown in FIGS. 2B, 2D and 2E, a refractive-index distribution in a plastic-molded lens is such that, generally, a refractive index at a peripheral portion of the lens is higher than that at a middle portion thereof.
Generally, when an optical scanning lens has such a refractive-index distribution inside thereof, actual optical characteristics thereof differ somewhat from xe2x80x98design optical characteristics of the optical scanning lens designed assuming that a refractive index therein is uniformxe2x80x99.
For example, when an optical scanning lens has a positive power, on average, a refractive index of a peripheral portion of the lens is higher than a refractive index of a middle portion thereof, and, such a refractive-index distribution functions to shift an actual position at which a beam spot to be formed on a surface to be scanned is formed xe2x80x98in direction in which the position goes away from a light deflector from a position determined in accordance with a designxe2x80x99.
A diameter of a beam spot by which an effective scanning range of a surface to be scanned is scanned changes as an image height changes depending on a curvature of field of an optical scanning lens. However, when a lens has such a refractive-index distribution therein, a diameter of a beam spot changes also due to an influence of the refractive-index distribution.
In FIG. 4, a vertical axis indicates a diameter of a beam spot and a horizontal axis indicates an amount of defocus (a difference between a position at which an image of a beam spot is formed (at which a light flux is gathered) and a position of a surface to be scanned). The vertical axis coincides with a surface of a photosensitive body as the surface to be scanned.
When an optical scanning lens has no refractive-index distribution therein and xe2x80x98a refractive index of the lens is uniform throughout the lensxe2x80x99, a relationship between an amount of defocus and a diameter of a beam spot is such that, as indicated by a broken line, the diameter of the beam spot is minimum at a position of a surface to be scanned (a position at which the amount of defocus is zero, actually, a position of a photosensitive body). However, when a refractive-index distribution exists, a relationship between an amount of defocus and a diameter of a beam spot is such that, as indicated by a solid line, the diameter of the beam spot at a position of a surface to be scanned is larger than that in accordance with a design (a cross point of the vertical axis and the broken line) due to xe2x80x98beam thickeningxe2x80x99
As materials of optical plastic lenses, mainly, acrylic resin, PC (polycarbonate) and polyolefin resin are known. Acrylic resin includes PMMA and alicyclic acrylic resin. Polyolefin resin includes ordinary polyolefin (such as polyethylene, polypropylene or the like) and alicyclic polyolefin.
FIG. 12 shows a list of optical characteristics of these resins.
A photoelasticity constant in the list of FIG. 12 can be used to determine whether double refraction of a lens formed by plastic molding is large or small. Acrylic resin is problematic because a moisture absorption is large although double refraction (photoelasticity constant) is small, and, in particular, a surface accuracy is likely to deteriorate as environment changes. Although PC (polycarbonate) has a high refractive index and a small moisture absorption, a photoelasticity constant thereof is very large and thereby double refraction is likely to develop, and wavefront aberration of a light flux transmitted thereby is likely to deteriorate.
Polyolefin resin has a small moisture absorption and a superior double refraction character. Therefore, recently, it is intended that polyolefin resin is used as a material of an optical scanning lens.
However, polyolefin resin has a relatively large mold shrinkage coefficient in comparison to other plastic materials, molding is somewhat difficult, and a refractive-index distribution is likely to develop unless molding conditions such as molding pressure, molding temperature and so forth are made to be the optimum ones.
An object of the present invention is to provide an optical scanning lens, a refractive index distribution of which is reduced to a level in which no problem occurs in optical characteristics, and to provide an optical scanning device using the optical scanning lens and an image forming apparatus using the optical scanning device.
An optical scanning lens according to the present invention is xe2x80x98an optical scanning lens used in a scanning and image forming optical system which gathers a light flux deflected by a light deflector in the vicinity of a surface to be scannedxe2x80x99.
As described above, xe2x80x98a scanning and image forming optical systemxe2x80x99 is an optical system which gathers a light flux deflected by a light deflector in the vicinity of a surface to be scanned, and, may consist of a single lens, may consist of a plurality of single lenses, or may consist of a combination of one or a plurality of single lens(es) and a specular surface (concave surface or convex surface) having a function of forming an image.
xe2x80x98An optical scanning lensxe2x80x99 is a lens used as a component of a scanning and image forming optical system, and one or a plurality of single lens(es) thereof is (are) arranged in the scanning and image forming optical system. When a scanning and image forming optical system consists of a single lens, the optical scanning lens itself is the scanning and image forming optical system.
An optical scanning lens is formed by xe2x80x98plastic molding of polyolefin resinxe2x80x99.
According to the present invention, the following condition is satisfied
0 less than |xcex94n(x)xe2x88x92min[xcex94n(x)]| less than 34xc3x9710xe2x88x925xe2x80x83xe2x80x83(A) 
where xcex94n(x) denotes a refractive-index distribution existing inside the lens, in a range which the light flux passes through, in the lens, and min[xcex94n(x)] denotes the minimum value of the xcex94n(x).
The above-mentioned xe2x80x98range which the light flux passes through, in the lensxe2x80x99 is a range which a light flux deflected by a light deflector passes through the optical scanning lens when being deflected.
According to another aspect of the present invention, the following condition is satisfied
0 less than |xcex94n| less than 8.5xc3x9710xe2x88x925xe2x80x83xe2x80x83(B) 
where, when xcex94n(x) denotes a refractive-index distribution existing inside the lens, in a range between approximately xc2x11 mm from a center of the light flux, in a range which the light flux passes through, in the lens, xcex94n denotes a coefficient of second order in xe2x80x98second-order least-square approximationxe2x80x99 of the xcex94n(x).
According to another aspect of the present invention, the following condition is satisfied
0 less than |xcex94n(x)xe2x88x92min[xcex94n(x)]| less than 34xc3x9710xe2x88x925xe2x80x83xe2x80x83(A) 
where xcex94n(x) denotes a refractive-index distribution existing inside the lens, in a range which the light flux passes through, in the lens, and min[xcex94n(x)] denotes the minimum value of the xcex94n(x), and, also, the following condition is satisfied
0 less than |xcex94n| less than 8.5xc3x9710xe2x88x925xe2x80x83xe2x80x83(B) 
where, when xcex94n(x) denotes a refractive-index distribution existing inside the lens, in a range between approximately xc2x11 mm from a center of the light flux, in a range which the light flux passes through, in the lens, xcex94n denotes a coefficient of second order in second-order least-square approximation of the xcex94n(x).
According to another aspect of the present invention, the following condition is satisfied
0.4xc3x9710xe2x88x925 less than |xcex94n(x)xe2x88x92min[xcex94n(x)]| less than 16xc3x9710xe2x88x925xe2x80x83xe2x80x83(C) 
where xcex94n(x) denotes a refractive-index distribution existing inside the lens, in a range which the light flux passes through, in the lens, and min[xcex94n(x)] denotes the minimum value of the xcex94n(x).
According to another aspect of the present invention, the following condition is satisfied
0.1xc3x9710xe2x88x925 less than |xcex94n| less than 4.0xc3x9710xe2x88x925xe2x80x83xe2x80x83(D) 
where, when xcex94n(x) denotes a refractive-index distribution existing inside the lens, in a range between approximately xc2x11 mm from a center of the light flux, in a range which the light flux passes through, in the lens, xcex94n denotes a coefficient of second order in second-order least-square approximation of the xcex94n(x).
According to another aspect of the present invention, the following condition is satisfied
0.4xc3x9710xe2x88x925 less than |xcex94n(x)xe2x88x92min[xcex94n(x)]| less than 16xc3x9710xe2x88x925xe2x80x83xe2x80x83(C) 
where xcex94n(x) denotes a refractive-index distribution existing inside the lens, in a range which the light flux passes through, in the lens, and min[xcex94n(x)] denotes the minimum value of the xcex94n(x), and, also, the following condition is satisfied
0.1xc3x9710xe2x88x925 less than |xcex94n| less than 4.0xc3x9710xe2x88x925xe2x80x83xe2x80x83(D) 
where, when xcex94n(x) denotes a refractive-index distribution existing inside the lens, in a range between approximately xc2x11 mm from a center of the light flux, in a range which the light flux passes through, in the lens, xcex94n denotes a coefficient of second order in second-order least-square approximation of the xcex94n(x).
In each aspect of the present invention, when the scanning and image forming optical system includes a plurality of single lenses, it is possible that the scanning and image forming optical system may include a lens(es) made of PC and/or acrylic resin, a glass lens(es) and/or the like, as a lens(es) other than the optical scanning lens of the plurality of single lenses.
An optical scanning device according to the present invention is xe2x80x98an optical scanning device which deflects a light flux from a light source, gathers the deflected light flux on a surface to be scanned as a beam spot by a scanning and image forming optical system, and performs optical scanning of the surface to be scannedxe2x80x99.
As xe2x80x98a light sourcexe2x80x99, various types of well-known ones can be used. In particular, a semiconductor laser is preferable to be used as a light source.
An optical scanning device according to the present invention is characterized in that any optical scanning lens according to the present invention is mounted as an optical scanning lens used in a scanning and image forming optical system.
It is possible that, in any optical scanning device, a light deflector which deflects a light flux from the light source is provided and the light deflector xe2x80x98has a deflection reflecting surface and deflects the light flux at a uniform angular velocityxe2x80x99, and the optical scanning lens xe2x80x98has a function of causing the scanning of the surface to be scanned to be performed at a uniform velocityxe2x80x99.
As the above-mentioned xe2x80x98light deflectorxe2x80x99, it is preferable to use a rotational polygonal (multi-surface) mirror, a rotational dihedral (bi-surface) mirror, or a rotational mono-surface mirror.
It is possible that, in the optical scanning device, an image is formed from the light flux from the light source in the vicinity of the deflection reflecting surface of the light deflector, the image being like approximately a line long in main scanning directions. For example, it is possible that a light flux from the light source is transformed into a light-flux form (any form of a parallel light flux, a convergent light flux and a divergent light flux is possible) suitable for a subsequent optical system by a coupling lens, and, from the thus-coupled light flux, a line image long in main scanning directions is formed in the vicinity of the deflection reflecting surface of the light deflector by a line-image forming optical system such as a cylinder lens. Thereby, it is possible to correct a surface inclination of the light deflector.
An image forming apparatus according to the present invention is xe2x80x98an image forming apparatus which performs optical scanning of a photosensitive surface of an image carrying body and thereby forms a latent image thereon, develops the latent image and thereby visualizes itxe2x80x99.
In an image forming apparatus according to the present invention, any optical scanning device according to the present invention is mounted as an optical scanning device which performs the optical scanning the photosensitive surface of the image carrying body as the surface to be scanned.
As xe2x80x98an image carrying bodyxe2x80x99, for example, a silver film for an original plate can be used. In this case, a printed image can be obtained as a result of development and fixing of a silver-film photographic process being performed on a formed latent image. An image forming apparatus in this case is xe2x80x98a digital plate making machinexe2x80x99.
It is possible that, the image forming apparatus is xe2x80x98an image forming apparatus in which the image carrying body is a photoconductive photosensitive body, after the photosensitive body being charged uniformly, an electrostatic latent image being formed thereon by the optical scanning, the thus-formed electrostatic latent image being developed so that a toner image is obtained, and the thus-obtained toner image being transferred and fixed onto a sheet-like recording mediumxe2x80x99. Thereby, a printed image is obtained. In this case, the image forming apparatus is xe2x80x98a digital copier, an optical printer, a laser plotter, a facsimile apparatus or the likexe2x80x99. As the above-mentioned sheet-like recording medium, transfer paper, a plastic sheet for an overhead projector, or the like can be used. A transfer of a toner image onto a sheet-like recording medium may be a transfer of a toner image from a photosensitive body to a recording medium directly, or may be a transfer via an intermediate transfer medium such as an intermediate transfer belt.
According to the present invention, it is possible to achieve novel optical scanning lens, optical scanning device and image forming apparatus.
An optical scanning lens according to the present invention is made of polyolefin resin which is superior in a moisture-absorption property and a double-refraction property, and has an internal refractive-index distribution controlled effectively, thereby being not likely to be affected by changes in environmental conditions such as temperature, humidity and so forth.
Further, an optical scanning device according to the present invention uses the above-mentioned optical scanning lens, and, thereby, it is possible to achieve an optical scanning device which is not likely to be affected by environmental fluctuation and is always satisfactory.
Furthermore, an image forming apparatus according to the present invention uses the above-mentioned optical scanning device, and, thereby, it is possible to achieve an image forming apparatus which is not likely to be affected by environmental fluctuation and is always satisfactory.
Other objects and further features of the present invention will become more apparent from the following detailed description when read in conjunction with the accompanying drawings.